In this article, we study the thermo-elastic vibration of axially functionally graded material (FGM) pipe conveying fluid considering temperature changes. The governing equation based on Euler–Bernoulli beam theory is solved by differential quadrature method. The FGM properties are defined by the property ratios and the volume fraction functions. Power volume fraction function and exponent volume fraction function are compared. We also use sigmoid volume fraction functions so that the exclusive influence of function distribution can be isolated from that of total material proportions. The property ratios’ effects of elasticity and thermo-elasticity gradient are also discussed. Based on the numerical results of first-order dimensionless frequencies and critical flow velocities, concerning thermo-elasticity gradient can theoretically change the stability of the pipe. And the influences of the pure distribution on the first-order critical flow velocities are much smaller than that of the varying total proportions of the component materials. These conclusions will hopefully be used as reference for FGM pipe designing and fabricating.

在本文中，我们研究了考虑温度变化的轴向功能梯度材料（FGM）输送流体的管道的热弹性振动。基于微分求积法求解基于欧拉-伯努利梁理论的控制方程。FGM特性由特性比和体积分数函数定义。比较了幂体积分数函数和指数体积分数函数。我们还使用S形体积分数函数，以便可以将函数分布的排他性影响与总材料比例的影响分开。还讨论了性能比对弹性和热弹性梯度的影响。根据一阶无量纲频率和临界流速的数值结果，从理论上讲，有关热弹性梯度的问题可以改变管道的稳定性。而且，纯分布对一阶临界流速的影响要远小于组分材料总比例变化的影响。这些结论有望为FGM管道的设计和制造提供参考。